The design of photonic crystal cavities takes inspiration from the periodic nature of atomic crystals and the effect on energy bands with allowed and disallowed states and uses the same framework to understand what happens if there is periodicity in refractive index. The effect of this periodicity is well known through the Bragg stack, which has been used to make mirrors out of dielectric materials. Bragg stacks are designed with the boundary condition that the Fresnel reflection at each interface of alternating high and low refractive index materials occurs at such distances that the fields interfere constructively towards the incident side of the stack thus maximizing reflection. It is possible to use transfer matrix methods to evaluate an expression relating the incident and the transmitted field and thus predict reflectance and transmission from such stacks. The spectral range where Bragg stacks are highly reflecting is called the stop band and is the photonic equivalent of an electronic bandgap. However the photonic bandgap in Bragg stacks is incomplete and only valid for TE fields and not for TM fields. 2D and 3D photonic crystals i.e. refractive index periodicity in 2 and 3 dimensions on the other hand can have complete bandgap.
These cavities are useful for studying light matter interaction in the two regimes of strong and weak coupling. In the strong coupling regime phenomena like Rabi Oscillations can be demonstrated and in the weak coupling regime effects like Purcell enhancement can be observed. In recent years interest in photonic crystal cavities has evolved from mere tools for studying fundamental phenomena such as the Purcell enhancement or Rabi oscillations, to use in actual optoelectronic devices such as electronically pumped lasers or pressure and chemical sensors. The fundamental benefit of the photonic crystal cavities is the use of dielectric materials which are mainly non lossy. This property allows for high quality factor cavities with reported figures as high as 106, which has not been possible with metallic cavities.
2D photonic and 1D photonic crystal cavities incorporating silicon nanocrystals have been demonstrated. However the designs of such cavities have not been provided for the material properties of silicon nanocrystals. It was shown that 1D nanobeam cavities are possible with quality factors as high as 25000 and mode volumes as low as 1.1(λ/n)3 using silicon rich oxide which has a refractive index of only n˜1.7, while others have studied 2D photonic crystals and showed Q factors of 300 with mode volume of 0.78(λ/n)3.
Vertical cavity surface emitting lasers (VCSELs) have been the dominant 1D cavity structure but more recently the horizontal nanobeam has become of interest as well. The nanobeam is a free-standing structure with periodic air holes serving as the low index material. An early prior art design of such structure is shown in FIG. 1 made in silicon. The periodicity of refractive index results in a stop band but in order to create a resonant mode, a defect must be introduced in this periodicity thus forming allowed photon states. Usually the defects are either a change in periodicity or size of an element and determine the allowed photon density of states, which is relevant for the strength of the light matter interaction. In this early design the defect was created by changing the period in the cavity center thus allowing a resonance with a quality factor of 280 at 1547 nm.
The condition for high reflection in a Bragg stack is:a=λ4n1+λ4n2  (1)an1=an2(n1+n2)  (1a)
Here ‘a’ is the periodic spacing with materials of refractive index n1 and n2. Further, an1 is the thickness of the material with refractive index n1. This is known as the quarter-wave stack as thickness of each material is equal to a quarter wavelength in that material. The estimated bandgap for the quarter-wave stack is given by:Δλ=4λπ arcsin(n2−n1n2+n1)  (2)
It can be seen from equation (2) that a higher refractive index contrast i.e. n2−n1 increases the bandgap. A high bandgap indicates a high inhibition of photons and is needed for ultrahigh quality factor cavities. This condition poses a problem for low refractive index materials like silicon rich oxide.
With the use of 1d nanobeam cavities high quality factors can be observed in low refractive materials. However for broad emitters like silicon nanocrystals or III-V compounds at room temperature what is needed is a 1d nanobeam photonic crystal cavity structure capable of relatively high quality factors with a ultra low mode volume.